class: center, middle, inverse, title-slide .title[ # 2023 Women in Statistics and Data Science Conference ] .subtitle[ ## Mortality Rates from Violent Deaths by Racial and Ethnic Groups in the United States, 2016-2020 ] .author[ ### <br>Ying-Ju Tessa Chen, PhD <br>(This is joint work with Dr. Tatjana Miljkovic.)<br><br> Associate Professor <br> Department of Mathematics<br> University of Dayton <br><br> <a href="https://twitter.com/ju_tessa"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg> <span class="citation">@ying-ju</span></a> <br> <a href="https://github.com/ying-ju/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> ying-ju</a> <br> <a href="mailto:ychen4@udayton.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"></path></svg> ychen4@udayton.edu</a><br> ] .date[ ### October 27, 2023 ] --- ## Background --- ## Objective We investigate the mortality rates by identifying violent manners of death in underrepresented communities relative to the white communities in the U.S. by studying the following: - Whether mortality rates for the identified violent manner of death differ between underrepresented communities and white communities in the U.S. - Whether sex, race, age and the manner of death are significant factors in determining violent mortality rates in the U.S. - The relative risk of specific manners of death, including suicide, homicide, legal intervention by police and other authorities, unintentional firearm–self-inflicted, and unintentional firearm–unknown-inflicted. --- ## Datasets Used .pull-left[ - NVDRS - Manners of Deaths - Year - State - Sex - Age - Race - Ethnicity .left[.footnote[.blue[National Violent Death Reporting System]] ]] .pull-right[ - CDC WONDER - Year - State - Gender - Age Group - Race - Population .left[.footnote[.blue[Wide-ranging ONline Data for Epidemiologic Research]]] ] --- ## Terminology for Race and Ethnicity used Across Sources <table> <thead> <tr> <th style="text-align:left;"> Race/Ethnicity </th> <th style="text-align:left;"> This Report </th> <th style="text-align:left;"> NVDRS </th> <th style="text-align:left;"> WONDER </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Race </td> <td style="text-align:left;"> Asian/Asian American </td> <td style="text-align:left;"> Asian/Pacific Islander </td> <td style="text-align:left;"> Asian and Pacific Islander </td> </tr> <tr> <td style="text-align:left;"> Race </td> <td style="text-align:left;"> Black/African American </td> <td style="text-align:left;"> Black or African American </td> <td style="text-align:left;"> Black or African American </td> </tr> <tr> <td style="text-align:left;"> Race </td> <td style="text-align:left;"> Native American/Alaska Indigenous Resident </td> <td style="text-align:left;"> American Indian/Alaska Native </td> <td style="text-align:left;"> American Indian and Alaska Native </td> </tr> <tr> <td style="text-align:left;"> Race </td> <td style="text-align:left;"> White </td> <td style="text-align:left;"> White </td> <td style="text-align:left;"> White </td> </tr> <tr> <td style="text-align:left;"> Ethnicity </td> <td style="text-align:left;"> Hispanic/Latino </td> <td style="text-align:left;"> Hispanic </td> <td style="text-align:left;"> Hispanic or Latino </td> </tr> </tbody> </table> --- ## NVDRS State Data - 27 States (43%) <style> .custom h2, 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/>Average Death in 2016-2020 <br />Suicide: 1310.6 deaths<br />Homocide: 368.6 deaths","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(255,255,255,1)","dash":"solid"},"fill":"toself","fillcolor":"rgba(0,123,255,1)","hoveron":"fills","name":"In Data","legendgroup":"In 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/>Average Death in 2016-2020 <br />Suicide: 1217.4 deaths<br />Homocide: 236.6 deaths","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(255,255,255,1)","dash":"solid"},"fill":"toself","fillcolor":"rgba(0,123,255,1)","hoveron":"fills","name":"In Data","legendgroup":"In 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(y) ","x"],"4d9c47a0a89":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- ## EDA <img src="data:image/png;base64,#./figures/Homicide_Race_Age.png" width="100%" style="display: block; margin: auto;" /> .caption[Homicide Mortality Rates Per 100,000 From 2016 To 2020 By Age Group And Race ] --- ## Motivation to Go Beyond Exploratory Data Analysis - Limitations of EDA - Importance of Statistical Modeling - Applications of Statistical Modeling - Conclusion --- ## Methodology - Negative Binomial GLM - `\(Y_i, i=1, 2, \ldots, N\)`: random variables for the number of deaths due to a violent event, and its realizations are denoted as `\(y_i, i=1, 2, \ldots, N\)`. - Assume `\(Y_i|\mu_i, r_i \sim NegBin(\mu_i, r_i), i=1, 2, \ldots, N\)` - `\(X_i'=(X_{1i}, X_{2i}, \ldots X_{pi})\)`: a `\(p\)`-dimensional vector of categorical factors with its realization `\(x_i'=(X_{1i}, x_{2i}, \ldots x_{pi})\)`, `\(i=1, 2, \ldots, N\)`. When modeling mortality rates, the Negative-Binomial GLM can be related to the linear model for the ratio response as follows: .center[ `\(\log \left(\frac{Y_i}{p_i}\right) = \beta_1 + \beta_2 x_{1i} + \beta_3 x_{2i} + \cdots + \beta_p x_{i, p-1},\)` ] where `\(p_i\)` represents the population count associated with the number of deaths `\(Y_i\)` for the `\(i\)`th level of aggregation. --- ## Statistical Analysis - GLM Modeling .pull-left-2[ .small[ <table class="table" style="margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> MODEL NAME (First 2 Characters) </th> <th style="text-align:center;"> FACTORS </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;width: 4cm; "> M1 </td> <td style="text-align:center;"> Year + State + Sex + Race (or Ethnicity) + Age Group </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M2 </td> <td style="text-align:center;"> State + Sex + Race (or Ethnicity) + Age Group </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M3 </td> <td style="text-align:center;"> Sex + Race (or Ethnicity) + Age Group </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M4 </td> <td style="text-align:center;"> Race (or Ethnicity) + Age Group </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M5 </td> <td style="text-align:center;"> Sex + Race (or Ethnicity) </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M6 </td> <td style="text-align:center;"> Race (or Ethnicity) </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M7 </td> <td style="text-align:center;"> Age Group </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M8 </td> <td style="text-align:center;"> Race (or Ethnicity) + Age Group + Age Group:Race (or Ethnicity) </td> </tr> <tr> <td style="text-align:left;width: 4cm; "> M9 </td> <td style="text-align:center;"> Age Group + Sex </td> </tr> </tbody> </table> ] ] .pull-right-2[ <img src="data:image/png;base64,#./figures/models.png" width="100%" style="display: block; margin: auto;" /> ] --- ## Analysis Of The Glm Models - `Step A:` The chi-square goodness-of-fit test (GOF) is applied to all GLM models and those that passed these test are further considered. - `Step B:` Model diagnostics are examined for all models. The diagnostic tools include the half-normal plot of residuals and the density plot. Diagnostic plots are analyzed along with the findings in step A. - `Step C:` All models are additionally tested for overdispersion using the R function check_overdispersion() from the R package performance (0.10.3) (Lüdecke et al. 2021), and those models that did not pass the test are disregarded if possible. - `Step D:` The likelihood-ratio test and Akaike information criterion (see Appendix C) are used to compare the pairs of models in the selected subsets of model space. - `Step E:` The investigation and selection of the most suitable model are based on balancing consistency and the results across all the above steps. - `Step F:` The most suitable selected GLM model is used to explain the results and findings of this study. --- ## Models Chosen for Suicide, Homicide, and Other <table> <thead> <tr> <th style="text-align:left;"> Model </th> <th style="text-align:center;"> Factors </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> M6-S-R </td> <td style="text-align:center;"> Race </td> </tr> <tr> <td style="text-align:left;"> M8-S-R </td> <td style="text-align:center;"> Age Group + Race + Age Group:Race </td> </tr> <tr> <td style="text-align:left;"> M5-S-E </td> <td style="text-align:center;"> Sex + Ethnicity </td> </tr> <tr> <td style="text-align:left;"> M2-H-R </td> <td style="text-align:center;"> State + Age Group + Sex + Race </td> </tr> <tr> <td style="text-align:left;"> M2-H-E </td> <td style="text-align:center;"> State + Age Group + Sex + Ethnicity </td> </tr> <tr> <td style="text-align:left;"> M2-O-R </td> <td style="text-align:center;"> State + Age Group + Sex + Race + Manner </td> </tr> <tr> <td style="text-align:left;"> M2-O-E </td> <td style="text-align:center;"> State + Age Group + Sex + Ethnicity + Manner </td> </tr> </tbody> </table> --- ## Relative Risk By Race Or Ethnicity .pull-left[ <img src="data:image/png;base64,#./figures/Risk_Race.png" width="100%" style="display: block; margin: auto;" /> .caption[No other fixed factors are used for suicide; fixed factors for homicide are state, age, and sex; fixed factors for “other" are state, age, sex, and manner.] ] .pull-right[ <img src="data:image/png;base64,#./figures/Risk_Ethnicity.png" width="100%" style="display: block; margin: auto;" /> .caption[Fixed factor for suicide is sex; fixed factors for homicide are state, age, and sex; fixed factors for “other” are state, age, sex, and manner.] ] --- ## Relative Risks By Ethnicity and Sex in Model M5-S-E <img src="data:image/png;base64,#./figures/Risk_M5SE.png" width="90%" style="display: block; margin: auto;" /> --- ## Wrap-Up ✅ Read text-files, binary files (e.g., Excel, SAS, SPSS, Stata, etc), json files, etc. online using <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#CE0037;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg> ✅ Scrape a webpage using <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#CE0037;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg> ✅ Understand when can we scrape data (i.e., `robots.txt`) --- ## Thanks .pull-left[ - Please do not hesitate to contact me (Tessa Chen) if you have questions pertaining to learning R or other languages. Please email me at <a href="mailto:ychen@udayton.edu"><i class="fa fa-paper-plane fa-fw"></i>&nbsp; ychen4@udayton.edu</a>. - Slides were created via the R package **xaringan**, with styling based on: * [xariganthemer](https://cran.r-project.org/web/packages/xaringanthemer/vignettes/xaringanthemer.html) package, and * Alison Hill's [@apreshill](https://github.com/apreshill/) CSS resources for customizing themes and fonts - The formatting of slides is provided by Dr. Fadel M. Megahed [@fmegahed](https://github.com/fmegahed). ] .pull-right[ <img src="data:image/png;base64,#./figures/Tessa_grey_G.gif" width="60%" style="display: block; margin: auto;" /> ] --- # Appendix - Suicide Models ## Coefficients: Suicide-Race, Model 6 (M6-S-R) <table> <thead> <tr> <th style="text-align:left;"> Variable </th> <th style="text-align:center;"> Relative Risk </th> <th style="text-align:center;"> Coefficients Esitmate </th> <th style="text-align:center;"> Coefficients Standard Error </th> <th style="text-align:center;"> Z Value </th> <th style="text-align:center;"> P Value </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Intercept </td> <td style="text-align:center;"> - </td> <td style="text-align:center;"> 2.95 </td> <td style="text-align:center;"> 0.01 </td> <td style="text-align:center;"> 197.77 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> <tr> <td style="text-align:left;"> Race R2 </td> <td style="text-align:center;"> 63% </td> <td style="text-align:center;"> -0.46 </td> <td style="text-align:center;"> 0.03 </td> <td style="text-align:center;"> -16.55 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> <tr> <td style="text-align:left;"> Race R3 </td> <td style="text-align:center;"> 76% </td> <td style="text-align:center;"> -0.27 </td> <td style="text-align:center;"> 0.03 </td> <td style="text-align:center;"> -7.77 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> <tr> <td style="text-align:left;"> Race R4 </td> <td style="text-align:center;"> 212% </td> <td style="text-align:center;"> 0.75 </td> <td style="text-align:center;"> 0.04 </td> <td style="text-align:center;"> 18.24 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> </tbody> </table> .right[.caption[Baseline for race is white (R1).]] <table> <thead> <tr> <th style="text-align:center;"> DF </th> <th style="text-align:center;"> DEVIATION </th> <th style="text-align:center;"> DISPERSION </th> <th style="text-align:center;"> AIC </th> <th style="text-align:center;"> P VALUE </th> <th style="text-align:center;"> 2-LIKELIHOOD </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> 5976 </td> <td style="text-align:center;"> 5931.16 </td> <td style="text-align:center;"> 1.87 </td> <td style="text-align:center;"> 37091.11 </td> <td style="text-align:center;"> 0.66 </td> <td style="text-align:center;"> -37081.1 </td> </tr> </tbody> </table> --- ## Diagnostic Plots for Suicide-Race Model 6 (M6-S-R) <br></br> <img src="data:image/png;base64,#./figures/suicide_race_M6.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Suicide-Ethnicity, Model 5 (M5-S-E) <table> <thead> <tr> <th style="text-align:left;"> Variable </th> <th style="text-align:center;"> Relative Risk </th> <th style="text-align:center;"> Coefficients Esitmate </th> <th style="text-align:center;"> Coefficients Standard Error </th> <th style="text-align:center;"> Z Value </th> <th style="text-align:center;"> P Value </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Intercept </td> <td style="text-align:center;"> - </td> <td style="text-align:center;"> 2.13 </td> <td style="text-align:center;"> 0.02 </td> <td style="text-align:center;"> 139.85 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> <tr> <td style="text-align:left;"> Ethnicity E2 </td> <td style="text-align:center;"> 72% </td> <td style="text-align:center;"> -0.33 </td> <td style="text-align:center;"> 0.02 </td> <td style="text-align:center;"> -14.00 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> <tr> <td style="text-align:left;"> Sex Male </td> <td style="text-align:center;"> 353% </td> <td style="text-align:center;"> 1.26 </td> <td style="text-align:center;"> 0.02 </td> <td style="text-align:center;"> 63.94 </td> <td style="text-align:center;"> &lt;0.001 </td> </tr> </tbody> </table> .right[.caption[Baseline for ethnicity is non-Hispanic/Latino (E1), for sex is female (F).]] <table> <thead> <tr> <th style="text-align:center;"> DF </th> <th style="text-align:center;"> DEVIATION </th> <th style="text-align:center;"> DISPERSION </th> <th style="text-align:center;"> AIC </th> <th style="text-align:center;"> P VALUE </th> <th style="text-align:center;"> 2-LIKELIHOOD </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> 3607 </td> <td style="text-align:center;"> 3690.25 </td> <td style="text-align:center;"> 4.31 </td> <td style="text-align:center;"> 25523.71 </td> <td style="text-align:center;"> 0.16 </td> <td style="text-align:center;"> -25515.71 </td> </tr> </tbody> </table> --- ## Diagnostic Plots for Suicide-Ethnicity Model 5 (M5-S-E) <br></br> <img src="data:image/png;base64,#./figures/suicide_ethnicity_M5.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Suicide-Race, Model 8 (M8-S-R) <img src="data:image/png;base64,#./figures/suicide_race_M8_coe.png" width="100%" style="display: block; margin: auto;" /> --- ## Diagnostic Plots for Suicide-Race Model 8 (M8-S-R) <br></br> <img src="data:image/png;base64,#./figures/suicide_race_M8.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Homicide-Race, Model 2 (M2-H-R) <img src="data:image/png;base64,#./figures/homicide_race_M2_coe.png" width="100%" style="display: block; margin: auto;" /> --- ## Diagnostic Plots for Homicide-Race Model 2 (M2-H-R) <br></br> <img src="data:image/png;base64,#./figures/homicide_race_M2.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Homicide-Ethnicity, Model 2 (M2-H-E) <img src="data:image/png;base64,#./figures/homicide_ethnicity_M2_coe.png" width="100%" style="display: block; margin: auto;" /> --- ## Diagnostic Plots for Homicide-Ethnicity Model 2 (M2-H-E) <br></br> <img src="data:image/png;base64,#./figures/homicide_ethnicity_M2.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Other-Race, Model 2 (M2-O-R) <img src="data:image/png;base64,#./figures/other_race_M2_coe.png" width="100%" style="display: block; margin: auto;" /> --- ## Diagnostic Plots for Other-Race Model 2 (M2-O-R) <br></br> <img src="data:image/png;base64,#./figures/other_race_M2.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]] --- ## Coefficients: Other-Ethnicity, Model 2 (M2-O-E) <img src="data:image/png;base64,#./figures/other_ethnicity_M2_coe.png" width="100%" style="display: block; margin: auto;" /> --- ## Diagnostic Plots for Other-Ethnicity Model 2 (M2-O-E) <br></br> <img src="data:image/png;base64,#./figures/other_ethnicity_M2.png" width="100%" style="display: block; margin: auto;" /> .right[.caption[Blue line: empirical density from the data; red line: density from the fitted model]]